Lv Chenwei, Zhang Ren, Zhai Zhengzheng, Zhou Qi
Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
School of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China.
Nat Commun. 2022 Apr 21;13(1):2184. doi: 10.1038/s41467-022-29774-8.
Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas these intriguing phenomena have been considered peculiar to non-Hermitian systems, we show that they can be naturally explained by a duality between non-Hermitian models in flat spaces and their counterparts, which could be Hermitian, in curved spaces. For instance, prototypical one-dimensional (1D) chains with uniform chiral tunnelings are equivalent to their duals in two-dimensional (2D) hyperbolic spaces with or without magnetic fields, and non-uniform tunnelings could further tailor local curvatures. Such a duality unfolds deep geometric roots of non-Hermitian phenomena, delivers an unprecedented routine connecting Hermitian and non-Hermitian physics, and gives rise to a theoretical perspective reformulating our understandings of curvatures and distance. In practice, it provides experimentalists with a powerful two-fold application, using non-Hermiticity to engineer curvatures or implementing synthetic curved spaces to explore non-Hermitian quantum physics.
量子系统通常被分为厄米特系统和非厄米特系统。从非厄米特趋肤效应到对边界条件的超敏感性等非凡的非厄米特现象已得到广泛研究。尽管这些有趣的现象被认为是非厄米特系统所特有的，但我们表明，它们可以通过平坦空间中的非厄米特模型与其在弯曲空间中可能是厄米特的对应模型之间的对偶性自然地解释。例如，具有均匀手性隧穿的典型一维（1D）链等同于它们在有或没有磁场的二维（2D）双曲空间中的对偶，并且非均匀隧穿可以进一步调整局部曲率。这种对偶性揭示了非厄米特现象的深刻几何根源，提供了一条连接厄米特物理和非厄米特物理的前所未有的途径，并产生了一种重新塑造我们对曲率和距离理解的理论视角。在实践中，它为实验人员提供了一种强大的双重应用，即利用非厄米性来设计曲率或实现合成弯曲空间以探索非厄米特量子物理。
